Mathematical model of ships convoy in delivery of goods

Abstract

Abstract This paper describes the ship convoys intended for mathematically modelling. The phenomenon essentially imitates the behaviour of a shoal of fish for several advantages. However, a control design is investigated to ascertain the factors influencing the fleet to navigate jointly without diversion or collision. Furthermore, the vessels are assumed to function independently, but are only assigned a common task of delivering goods. The control design process employs an optimal method known as the Pontryagin Maximum Principle, and the model implemented is generally applied to marine vessels. Meanwhile, the control equation utilizes the Nomoto’s model. In addition, the ship model supports the rudder input responsible for the change in the direction of motion. Also, this study exposes a functional cost pattern describing the joint tasks and further models the ship convoys for optimum control. The numerical simulation provides a detailed summary of the applied optimal process to solve the problems encountered in deliveries.